S2 orbit deviates from Keplerian ellipse

[Strange]

Thanks

 

That is clear

https://imagine.gsfc.nasa.gov/features/yba/CygX1_mass/gravity/sun_mass.html

 

So,we can calculate Sun mass directly from Earth/Sun orbit without any info about Earth or moon mass.

 

However, it must be perfect Keplerian ellipse.

How that impact S2?

 

 

You have just agreed that the moon's orbit is not a perfect ellipse. And yet we can still use it to calculate the mass of the sun.

 

The case of S2 is slightly more complex, as Janus says, because the orbit does not average out to an ellipse (as the moon's does). But it is still possible to determine how much it deviates from an ellipse and use that to calculate the extra mass that is affecting the orbit at various points (as the paper your referenced has done).

 

Unless you can show a flaw in their mathematics, I think you will just have to accept their results (even if you are not able to understand it).

Edited April 4, 2017 by Strange

[David Levy]

The difference between the Moon-Earth example and S2 is that for the Moon, the total mass effecting its trajectory at an given moment is a constant. And while the Moon's actual trajectory relative to the Sun doesn't perfectly follow the Keplerian Eclipse it does vary around one. (average out the path of the moon and you get a Keplerian Eclipse.

 

 

With S2, the mass effecting its trajectory at any given point of its orbit is not a constant, as this image demonstrates:

S2.gif

 

The red circle is Sag A, the larger pink circle is the extra mass distributed around Sag A. The Blue ellipse is S2's orbit. At point A,the mass effecting S2's trajectory is that of Sag A plus that part of the extra mass closer to Sag A than it is (enclosed by the innermost yellow circle. At either of the points B it is Sag A plus the mass enclosed by the next yellow circle. The same holds for points C and D. Thus as S2 moves in and out from Sag A in its orbit, the mass effecting it changes. This causes a departure from a Keplerian Eclipse in a number of ways.

 

Thanks Janus

 

Your explanation is very interesting.

It's the first time that I get such explanation about gravity.

So it acts as a sinusoidal gravity wave going up and down as it cross different mass density zones.

Do we have any other example which could confirm this idea?

I had the impression that there could be some sort of tidal but not that kind of gravity change.

In any case, those different densities must be quite neglected comparing to Sgr A* mass (less than 1%).

"the strongest constraint that can be placed on these remnants is that their total mass comprises less than one percent of the mass of the supermassive black hole."

Therefore, how could it be that there is so severe impact on S2 Keplerian ellips?

 

Please look again on the following Diagram.

http://www.universetoday.com/wp-content/uploads/2010/08/nature01121-f2.22.jpg

We can see clearly that Sgr A* is not located at a symmetric point in that ellipse. (It is located at the bottom left side)

However, in your diagram the red circle - which represents Sgr A* , is fully symmetric.

Hence, how can we use an asymmetric point as a center of the ellipse?

You have just agreed that the moon's orbit is not a perfect ellipse. And yet we can still use it to calculate the mass of the sun.

The Sun is located perfectly at a symmetric point of the moon orbit ellipse.

Edited April 4, 2017 by David Levy

[Strange]

This paper describes how they determine the orbits of all the S stars, and the error margins associated with those. The second half of the paper (section 5 on page 16 onwards) describes how they determine the mass distribution (or other relativistic effects) that can produce the observed orbits.

https://arxiv.org/abs/0810.4674

 

I don't think there is the sort of simple answer you seem to be looking for.

[David Levy]

Thanks

 

It is stated: Draft version October 26, 2008

Is there any more updated data?

[Strange]

This is the published version: http://iopscience.iop.org/article/10.1088/0004-637X/692/2/1075/meta

[David Levy]

This paper describes how they determine the orbits of all the S stars, and the error margins associated with those. The second half of the paper (section 5 on page 16 onwards) describes how they determine the mass distribution (or other relativistic effects) that can produce the observed orbits.

https://arxiv.org/abs/0810.4674

 

If I understand it correctly, the aim of this article is to prove that Sgr A*.is the real S2 center of mass.

However, it seems to me that 2002 data contradicts this requirement:

In 2002 S2 was at the closest position to Sgr A*. (nearly coincident).

"In 2002, S2 was positionally nearly coincident with Sgr A* and thus confused with the NIR counterpart of the MBH."

Actually this kind of nearly coincident between S2 and Sgr A* could negativly effect the requirment for center of mass in Keplerian ellips.

In any case, based on the pure data from 2002 it seems that there is no fit:

"From this analysis, it is clear that the weight of the 2002 data will influence the resulting orbit fits, since these points will systematically change the orbit figure at its pericenter. At the same time we have no plausible explanation for the increase in brightness and the systematic residuals in the 2002 data; in particular a confusion event seems unlikely. Thus, it is clear that using the 2002 data will affect the results, but we cannot decide whether it biases towards the correct solution or away from it.

 

Therefore we use in the following two options: a) we include the 2002 data with the increased error bars; b) we completely disregard the 2002 data of S2."

Therefore, it was decided to fix the data of 2002 as follow:

Fig. 10.— The 2002 data of S2. The grey symbols show the measured positions, the errors are as obtained from the standard analysis and are not yet enlarged by the procedure described in section 3.5. The black dots are the positions predicted for the observation dates using an orbit fit obtained from all data other than 2002. The blue shaded areas indicate the uncertainties in the predicted positions resulting from the uncertainties of the orbital elements and of the potential, taking into account parameter correlations.

After fixing the data, they got better fit:

"From the numbers it seems that the fit excluding the 2002 data agrees better with the expectations for the coordinate system (equation 4) than the fit including it."

It is also stated:

"Systematic problems of the coordinate system could be absorbed into the orbital fitting by allowing the center of mass to have an offset from 0/0 and a non-zero velocity, at the cost of not being able to test the coincidence of the center of mass with radio Sgr A*.

From this analysis, it is clear that the weight of the 2002 data will influence the resulting orbit fits, since these points will systematically change the orbit figure at its pericenter.

I wonder how could it be that the center of mass has an offset and a non zero velocity.

 

Those are key requirements from any center of mass.

If it has velocity and offset – how can we use it as a center of mass?

Edited April 4, 2017 by David Levy

[Strange]

 

If I understand it correctly, the aim of this article is to prove that Sgr A*.is the real S2 center of mass.

 

 

Not really. It is to understand all the masses that affect the orbits of a number of stars (I think they look at 6 stars in detail). As well as to check that the predictions of GR match what we see.

 

 

I wonder how could it be that the center of mass has a non zero velocity.

 

It depends on the coordinate system used.

 

I'm afraid that the details of that paper are beyond my understanding so you are on your own here.

[David Levy]

With regards to the distance between S2 and Sgr A* in 2002

 

In 2002 S2 was at the closest position to Sgr A*. (nearly coincident).

 

". In 2002, S2 was positionally nearly coincident with Sgr A* and thus confused with the NIR counterpart of the MBH. Typically, Sgr A* is fainter than mK = 17 and thus the extra-light from Sgr A* in quiescence is not sufficient to explain the observed increase in brightness of S2. However, Sgr A* is known to exhibit flares that can reach a brightness level that could account for the observed increase in brightness"

 

So, when S2 was nearly coincident with Sgr A* its brightness increased significantly.

 

One of the explanation for that was that the extra brightness came from Sgr A*:

 

" 4. Loeb (2004) proposed that the stellar winds of early-type stars passing their pericenters close to the MBH could alter the accretion flow onto Sgr A*. Such an event would produce a change in the brightness of Sgr A* on the timescale of months, compatible with Figure 8. However, Martins et al. (2008) showed that the mass loss rate of S2 is too low for this mechanism to work."

 

So, does it mean that S2 and Sgr A* were exactly at the same spot?

 

Otherwise, Loeb would not even consider an option that the extra light came out of Sgr A* which was at the same spot as S2.

 

If so, why they claim nearly coincident? why not Fully coincident?

 

And if it was so close, why they didn't collide?

 

How could it be that the Sgr A*with its all of its Huge mass and gravity power didn't eat S2?

 

In any case, in fig 10 it is stated that the scientists fixed that position of S2.

 

"Fig. 10.— The 2002 data of S2. The grey symbols show the measured positions, the errors are as obtained from the standard analysis and are not yet enlarged by the procedure described in section 3.5. The black dots are the positions predicted for the observation dates using an orbit fit obtained from all data other than 2002. The blue shaded areas indicate the uncertainties in the predicted positions resulting from the uncertainties of the orbital elements and of the potential, taking into account parameter correlations."

 

However, Sgr A* was exactly at the same position as S2.

 

So, why our scientists decided to fix the data only for S2?

 

If there is an error as it is stated by our scientists, than this error should also apply to Sgr A* position.

 

Hence, why they only adjust S2 with the maximal error threshold while they didn't move Sgr A* accordingly to the selected maximal error margin?.

 

[swansont]

 

So, does it mean that S2 and Sgr A* were exactly at the same spot?

 

...

 

And if it was so close, why they didn't collide?

 

 

What does that mean, with non-point objects? If I stand on a football/soccer pitch in the penalty area, am I in the exact same spot as the pitch. Now I move to the center line. Same question.

 

I stand a near the sideline, but your optics don't allow you to resolve anything smaller than a meter. Am I standing inside or outside of the pitch? How would you describe my position?

 

This also ignores the fact that we are viewing a 3-D system, but observations are in 2D.

[Strange]

There is also the limited resolution and accuracy of observations to take into account. For example, this page (http://www.astrophysicsspectator.com/tables/MilkyWayCentralStars.html) says that the stars can be observed with a resolution of 0.025 arc seconds. That is about 200 AU, which is many, many times larger than the star.

Also, they could appear to be (nearly) coincident even if they are a long way away from each other if one is in front of or behind the other.

[Janus]

Please look again on the following Diagram.

http://www.universetoday.com/wp-content/uploads/2010/08/nature01121-f2.22.jpg

We can see clearly that Sgr A* is not located at a symmetric point in that ellipse. (It is located at the bottom left side)

A clue here can be taken from the legends on the top and side of the diagram. Note that they are labeled in right ascension and declination, which are measurements of angle. This indicates that this diagram is made of the orbit based on how it is seen from Earth, and not as seen looking "straight down" at the orbit. This can result in looking at the orbit from a angle, and give a false impression.

Here is an image of a Keplerian ellipse as viewed from such an angle. The blue dot is actually at a focus and is on the major axis and at a symmetric point of the ellipse. It appears off-center because, due to the viewing angle, What visually looks like the major axis in the image is not so in fact. It just appears so due to fore-shortening caused by the direction the ellipse is viewed from.

 

 

 

I believe this is what causes Sag A to appear off center-line in your linked image and not an actual displacement relative to the orbit.

[David Levy]

This also ignores the fact that we are viewing a 3-D system, but observations are in 2D.

 

Well it is even more complicate

 

In a kepler orbit the center of mass must be located at the same plate as the orbit itself.

https://en.wikipedia.org/wiki/Kepler_orbit#/media/File:Kepler_orbits.svg

 

Therefore, we are looking on a 2D orbit system which is located in a 3D space by a 2D observation.

 

Also, they could appear to be (nearly) coincident even if they are a long way away from each other if one is in front of or behind the other.

 

So, you claim that we can see one in the front while the other one is located behind the other.

However, if I understand it correctly, in order to achieve it, Sgr A* can't be located at S2 orbit cycle plate

 

 

A clue here can be taken from the legends on the top and side of the diagram. Note that they are labeled in right ascension and declination, which are measurements of angle. This indicates that this diagram is made of the orbit based on how it is seen from Earth, and not as seen looking "straight down" at the orbit. This can result in looking at the orbit from a angle, and give a false impression.

Here is an image of a Keplerian ellipse as viewed from such an angle. The blue dot is actually at a focus and is on the major axis and at a symmetric point of the ellipse. It appears off-center because, due to the viewing angle, What visually looks like the major axis in the image is not so in fact. It just appears so due to fore-shortening caused by the direction the ellipse is viewed from.

 

s2_1.gif

 

 

I believe this is what causes Sag A to appear off center-line in your linked image and not an actual displacement relative to the orbit.

 

Well, I have tried all the possibilities for a 2D ellips, while the center is located at the same plate of the orbit.

Unfortunately, I couldn't get a result which is similar to S2 orbit shape with a similar asymmetric location of center of mass.

However, once the Sgr A* is moved outside the orbit plate than you get it immediately.

So, can we understand that Sgr A* is not located on S2 orbit plate?

 

Edited April 5, 2017 by David Levy

[Strange]

 

Well it is even more complicate

 

In a kepler orbit the center of mass must be located at the same plate as the orbit itself.

https://en.wikipedia.org/wiki/Kepler_orbit#/media/File:Kepler_orbits.svg

 

Therefore, we are looking on a 2D orbit system which is located in a 3D space by a 2D observation.

 

 

That is not "even more complicated". That is exactly what was explained.

 

 

 

So, you claim that we can see one in the front while the other one is located behind the other.

 

I didn't claim anything. I was just pointing out that we can only see things in 2D and so cannot resolve the Z (depth) direction at all.

 

 

However, if I understand it correctly, in order to achieve it, Sgr A* can't be located at S2 orbit cycle plate

 

I'm afraid I don't understand that at all. (Although, we can be fairly certain that anything you write beginning with "if I understand it correctly..." is wrong.)

 

 

 

Well, I have tried all the possibilities for a 2D ellipse

 

How did you try this? Can you show the results you got?

[swansont]

The point was that the orbital plane (not plate) could be tilted with respect to us.

[Janus]

Well, I have tried all the possibilities for a 2D ellips, while the center is located at the same plate of the orbit.

Unfortunately, I couldn't get a result which is similar to S2 orbit shape with a similar asymmetric location of center of mass.

However, once the Sgr A* is moved outside the orbit plate than you get it immediately.

So, can we understand that Sgr A* is not located on S2 orbit plate?

It just took a little fiddling of the viewing angle of the orbit of S2 (basing the ellipse on S2's eccentricity) to get this image.

 

 

Which is very close to to the one you provided. Sag A is at the focus and in the plane of the orbit. (The green line represents the true major axis of the orbit.) You are just viewing the orbit from an angle other than 90 degrees from the plane of the orbit.

It is pretty clear that some fine-tuning, you could create an exact copy of the image you gave without moving Sag A off the Semi-major axis or off the orbital plane.

Further evidence that the offset in the image is due to viewing angle and not due to a physical displacement of Sag A relative to the orbit.

 

This image is pretty much the clincher.

https://en.wikipedia.org/wiki/Sagittarius_A*#/media/File:Galactic_centre_orbits.svg

 

It shows a number of the orbits of stars around Sag A. Not how the orbit of S2 looks like the image you linked to. The other orbits at different angles. S14 is of particular interest, it has an eccentricity of 0.9389, which would give it a minor axis a bit over a third the length of its major axis. In the image the orbit is shown quite a bit flatter than this, so it is obvious that we are viewing it from an angle.

From this is is pretty clear that your image of S2's orbit is as from our perspective and that we are viewing it from some angle that causes an apparent but not real offset of Sag A.

Edited April 5, 2017 by Janus

[David Levy]

It just took a little fiddling of the viewing angle of the orbit of S2 (basing the ellipse on S2's eccentricity) to get this image.

 

Thanks Janus

In the article it is stated that S2 and Sgr A* were - "nearly coincident". This isn't the case in your fig.

However, the 2002 data dilemma with regards to S2 center of mass had been introduced deeply by our scientists.

Please see the following:

https://arxiv.org/pdf/0810.4674.pdf

 

1. Disregard the 2002 data of S2 - "Thus, it is clear that using the 2002 data will affect the results, but we cannot decide whether it biases towards the correct solution or away from it. Therefore we use in the following two options: a) we include the 2002 data with the increased error bars; b) we completely disregard the 2002 data of S2."

 

So, if the 2002 data was correlated with the scientists expectations of fitting S2 central mass into the Sgr A*, they wouldn't consider those two options, especially not to disregards that data.

Hence, it is clear that based on the pure 2002 - There is no fit!!!

That is my understanding from that indirectly statement.

2. Increased error bars - So, in order to set the fit, our scientists select the option to increase the error bars on 2002 data to its maximal positions.

We see the impact o that "increased error bars" in Fig 10:

"Fig. 10.— The 2002 data of S2. The grey symbols show the measured positions, the errors are as obtained from the standard analysis and are not yet enlarged by the procedure described in section 3.5. The black dots are the positions predicted for the observation dates using an orbit fit obtained from all data other than 2002. The blue shaded areas indicate the uncertainties in the predicted positions resulting from the uncertainties of the orbital elements and of the potential, taking into account parameter correlations."

So they have shift S2 location with the maximal error bar in order to set the fit.

However, error bars works in all directions. Hence, technically, if we would shift S2 location just to the other side at the same error bar value we could find that Sgr A* is already outside the S2 orbit plane.

 

Therefore, let me ask the following:

 

Please look again on fig 10. Let's set a circle around the real location of S2 (based on 2002 data) with a radius of the maximal error resolution. Now, what is the chance that S2 should be moved to those selected new points out of all the other possibilities (based on the maximal error resolution)? I would assume that from statistical point of view it is very low! Therefore, I wonder why our scientists decided to set the error bar just in the amplitude and direction which fits their expectation.

 

3. Why they only consider those two options? Why they do not consider that there is a possibility that 2002 data is correct? Why they couldn't ask themselves - could it be that there is no fit? Why always our scientists try to fit the evidences to their expectations?

 

4. Offset and non zero velocity- Even after fixing the 2002, they have found that there is an offset and non zero velocity between S2 center of mass and Sgr A*. This is a clear violation of the basic requirements from any sort of Keplerian ellips. How can we accept it?

5. Hiding 2002 data dilemma from the Abstract -

In the abstract of that article it is stated:

 

"We present the results of 16 years of monitoring stellar orbits around the massive black hole in center of the Milky Way using high resolution near-infrared techniques. This work refines our previous analysis mainly by greatly improving the definition of the coordinate system, which reaches a longterm astrometric accuracy of ≈ 300 µas, and by investigating in detail the individual systematic error contributions. The combination of a long time baseline and the excellent astrometric accuracy of adaptive optics data allow us to determine orbits of 28 stars, including the star S2, which has completed a full revolution since our monitoring began."

 

Not even one word about the huge dilemma of 2002 data. They are proud of their accuracy, but they have forgotten to mention that directly based on the 2002 Data there is no fit! Actually just based on the very poor resolution, they could set some sort of a fit!!!

 

In other words, in the article they use their poor accuracy to set the fit, while in the abstract they highlight their excellent accuracy.

 

So, why they are so proud with this accuracy if in the article it is stated clearly that they have to shift S2 position to the maximal error bar in order to set a fit (and even with that fit they still have a relative offset and non zero velocity)?

6. New S2 data –

We are already 15 years after 2002. Soon, S2 should complete one more cycle and come close to Sgr A*. In those 15 years we have improved our accuracy. So where is the updated data???

7. Other S0 stars:

Why we just set the calculation on S2? what about all the others? Did we try to evaluate Sgr A* mass by one of the other S0 star orbit?

8. Why our scientists are in panic to prove that Sgr A* is the only valid option for S2 center of mass?

What could be the disaster if we will discover that it isn't?

Why it was so difficult for them to say clearly that based on pure 2002 data there is no fit?

Edited April 6, 2017 by David Levy

[David Levy]

O.K.

 

I assume that by now it's clear for all of us that based on 2002 data there is no fit.

It means that S2 center of mass is not Sgr A*.

 

Few questions:

 

1. a. Why our scientists refused to accept 2002 Data as is (although they were very proud with their accuracy)?

b. Why it was so important for them to prove a fit against the evidences?

c. Why they do not introduce new updated data on S2 orbit?

d. Why they do not set other S0 stars calculations for center of mass?

 

2. What could be the impact of that non fit discovery?

Edited April 7, 2017 by David Levy

[Strange]

8. Why our scientists are in panic to prove that Sgr A* is the only valid option for S2 center of mass?

What could be the disaster if we will discover that it isn't?

 

Please provide a reference to scientists bing in a panic? Where di you read this?

I assume that by now it's clear for all of us that based on 2002 data there is no fit.

It means that S2 center of mass is not Sgr A*.

 

No. That is not clear to anyone.

[David Levy]

No. That is not clear to anyone.

 

So can you please send your reply with regards to all the above points 1-8 ?

 

In any case, based on your understanding, why our scientists had to consider the following two options?:

"a) we include the 2002 data with the increased error bars;

b) we completely disregard the 2002 data of S2."

Why they couldn't use 2002 data as is?

Edited April 7, 2017 by David Levy

[Strange]

 

So can you please send your reply with regards to all the above points 1-8 ?

 

 

Easy: I don't know.

 

However, I don't assume that because I don't know, the experts must be wrong. That would be insane, wouldn't it?

[Klaynos]

Looking at the quotes here it looks like they didn't use the 2002 data because the measurement accuracy was poorer. Therefore including this data would increase the errors on the outcome (error analysis can show you how this works).

 

David, I've notice across several of your post that you seem to be unfamiliar with errors and precision in experimental physics. If suggest some readding around this. John R. Taylor's Introduction to Error Analysis is the book i normally suggest.

[David Levy]

Easy: I don't know.

 

However, I don't assume that because I don't know, the experts must be wrong. That would be insane, wouldn't it?

 

 

Well, if you don't know, than technically you can't reject my conclusion.

However, I assume that we all have some sort of basic common sense.

So, please try to answer the following simple questions:

1. Assuming that 2002 data of S2 meets perfectly the fit between S2 center of mass and Sgr A*;

Do you think that our scientists would consider to: completely disregard the 2002 data of S2 or to include the 2002 data with the increased error bar?

Please - only Yes or No

("I don't know" - is not a valid answer)

2. What is the meaning of: "increased error bar" message?

The meaning of "Error bar" is quite clear by google:

"a line through a point on a graph, parallel to one of the axes, which represents the uncertainty or error of the corresponding coordinate of the point."

So I assume that this is based on our accuracy. Hence, each accuracy level associates with some sort of error bar level.

However, when we say "Increased error bar" - what does it mean?

The meaning by cambridge dictionary.

http://dictionary.cambridge.org/dictionary/english/increase?q=Increased+

Increased - to (make something)become larger in amount or size:

The cost of the project has increased dramatically/significantly since it began.

So could it be that increased error bar" means higher/larger error bar?

In other words - could it be that our scientists are using higher error bar level than the permited accuracy?

 

Edited April 7, 2017 by David Levy

[Strange]

Well, if you don't know, than you technically can't reject my conclusion.

 

 

As your "conclusion" is based on nothing but random guesses (no evidence, no theory, nothing) I don't have any problem rejecting it.

 

 

 

 

Assuming that 2002 data of S2 meets perfectly the fit between S2 center of mass and Sgr A*;

 

Do you think that our scientists would consider to: completely disregard the 2002 data of S2 or to include the 2002 data with the increased error bar?

 

You are asking what they would have done if the data had been different ?

 

I guess they might have done something different.

[David Levy]

Looking at the quotes here it looks like they didn't use the 2002 data because the measurement accuracy was poorer. Therefore including this data would increase the errors on the outcome (error analysis can show you how this works).

 

Not at all!

 

It is not stated anywhere in the article that the measurement accuracy in 2002 was poorer than the average.

They claim clearly that In order to set the fit, they had to disregard 2002 data of S2 or to increase the error bar level.

Therefore, it is clear that based on 2002 measurement + the maximal permitted accuracy they didn't get any fit.

 

Just after increasing the error bar above the maximal permitted level they have got some sort of fit.

 

However, even this fit includes offset and non zero velocity of the central point of mass.

 

This by itself is a key violation for Keplerian ellipse.

One more question -

Why is it so important for the scientists to prove that S2 center of mass is Sgr A*?

Edited April 7, 2017 by David Levy

[swansont]

O.K.

 

I assume that by now it's clear for all of us that based on 2002 data there is no fit.

It means that S2 center of mass is not Sgr A*.

 

 

 

The orbital period is ~15 years. A single year's worth of data is not the basis for the fit.

could it be that our scientists are using higher error bar level than the permited accuracy?

 

What, pray tell, is a permitted accuracy?

 

I agree with Strange. Measurement, errors and precision are something to be added to the list of what you need to study before you can properly tackle this kind of analysis.